Coefficient of Variation (CV)

Dimensionless dispersion measure: the rolling population standard deviation divided by the rolling mean. Scales StdDev by the price level so two assets at very different price magnitudes can be compared directly. Higher CV = more relative variability.

Quick reference

Item	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	[0, ∞)
Default parameters	period required
Warmup period	period
Interpretation	Cross-instrument-comparable volatility measure

Formula

mean = (1/n) · Σ price
sd   = √( (1/n) · Σ price² - mean² )      (population StdDev)
CV   = sd / mean

Returns 0.0 when mean is zero (avoids NaN). See crates/wickra-core/src/indicators/coefficient_of_variation.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 1	Rolling window.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Standard binding shapes.

Warmup

warmup_period() == period.

Edge cases

• Mean = 0. Returns 0.0.
• Constant input. SD = 0 → CV = 0.
• Negative mean. CV uses raw mean, so result can be negative if you're feeding signed data with negative mean (rare with prices).
• Reset. Clears running sums.

Examples

Rust

use wickra::{BatchExt, CoefficientOfVariation, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..50)
        .map(|i| 100.0 + (f64::from(i) * 0.3).sin() * 5.0)
        .collect();
    let mut cv = CoefficientOfVariation::new(20)?;
    println!("row 30 = {:?}", cv.batch(&prices)[30]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 15, 50)) * 5
cv = ta.CoefficientOfVariation(20)
print(cv.batch(prices)[30])

Node

const wickra = require('wickra');
const cv = new wickra.CoefficientOfVariation(20);
const prices = Array.from({ length: 50 }, (_, i) => 100 + Math.sin(i * 0.3) * 5);
console.log(cv.batch(prices)[30]);

Streaming

use wickra::{CoefficientOfVariation, Indicator};

let mut cv = CoefficientOfVariation::new(252).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = cv.update(px) {
        // v is comparable across instruments with different price scales
    }
}

Interpretation

• Cross-instrument comparison. CV = 0.05 on a $10 stock (SD = $0.50) is the same volatility as CV = 0.05 on a $1000 stock (SD = $50). Unlike raw StdDev, CV is comparable.
• Volatility regime. Rising CV = increasing relative volatility. Falling CV = compressing volatility (often precedes a breakout).
• Pair with mean. A high CV with low mean = noisy and going nowhere; high CV with high mean trend = volatile trend.

Common pitfalls

• Negative-mean inputs. CV on signed return series with negative mean is misleading. Use absolute price for CV; StdDev / mean of returns gives a different statistic (volatility-to-drift ratio).
• Period choice. Same as StdDev — too-short windows are noisy.

References

• Standard statistics textbook measure; documented in any introductory statistics text.

See also

• StdDev — the numerator.
• Variance — squared cousin.
• HistoricalVolatility — return-based volatility alternative.
• Indicators-Overview — full taxonomy.